Problem: A circle with area $100\pi$ has a sector with a $84^\circ$ central angle. What is the area of the sector? ${100\pi}$ $\color{#9D38BD}{84^\circ}$ ${\dfrac{70}{3}\pi}$
Answer: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{84^\circ}{360^\circ} = \dfrac{A_s}{100\pi}$ $\dfrac{7}{30} = \dfrac{A_s}{100\pi}$ $\dfrac{7}{30} \times 100\pi = A_s$ $\dfrac{70}{3}\pi = A_s$